Question

Hello, I do not anderstand this at all. I have been working on radicals and stuff, but this goes way above my head. Please help.

Thank you so much! 100 points!

Solve for the following equation step by step and justify your steps when using an exponential property.

Answer 1

x =
`(5)/(7)`

Explanation:

We can start simplifying this equation by expanding the parenthesis and cross multiplying.

`(7^x)^4 = (7^2 * 7^3)/(7^(3x)) = \\\\\\7^(4x) = (7^5)/(7^(3x))\\\\\\7^5 = 7^(7x)\\\\\\`

The exponent 5 and 7x are equal:

`\longmapsto`Divide both sides by 7

`5 = 7x\\\\x = \frac57`

-Chetan K

Answer 2

• 5/7

Explanation:

Use identities:

• 
  `(a^b)^c = a^(bc)\\a^ba^c=a^(b+c)\\a^b/a^c=a^(b-c)\\a^b=a^c -->b = c`

Solve as below:

• (7ˣ)⁴ = 7² · 7³ / 7³ˣ
• 7⁴ˣ = 7⁵ / 7³ˣ
• 7⁴ˣ = 7⁵ ⁻ ³ˣ
• 4x = 5 - 3x
• 4x + 3x = 5
• 7x = 5
• x = 5/7